Bayesian hypothesis testing leverages posterior probabilities, Bayes factors, or credible intervals to assess characteristics that summarize data. We propose a framework for power curve approximation with such hypothesis tests that assumes data are generated using statistical models with fixed parameters for the purposes of sample size determination. We present a fast approach to explore the sampling distribution of posterior probabilities when the conditions for the Bernstein-von Mises theorem are satisfied. We extend that approach to facilitate targeted sampling from the approximate sampling distribution of posterior probabilities for each sample size explored. These sampling distributions are used to construct power curves for various types of posterior analyses. Our resulting method for power curve approximation is orders of magnitude faster than conventional power curve estimation for Bayesian hypothesis tests. We also prove the consistency of the corresponding power estimates and sample size recommendations under certain conditions.

翻译：贝叶斯假设检验利用后验概率、贝叶斯因子或可信区间来评估数据特征的汇总结果。我们提出了一种针对此类假设检验的功效曲线逼近框架，该框架假设数据基于参数固定的统计模型生成，从而确定样本量。我们发展了一种快速方法，用于在满足伯恩斯坦-冯·米塞斯定理条件时探索后验概率的抽样分布。我们将该方法进一步扩展，以支持针对每个探索样本量从后验概率的近似抽样分布中进行目标采样。这些抽样分布被用于构建各类后验分析的功效曲线。与贝叶斯假设检验的传统功效曲线估计方法相比，我们最终得到的功效曲线逼近方法在速度上实现了数量级提升。此外，我们还在特定条件下证明了相应功效估计与样本量推荐结果的一致性。